ADVANCED SUBSIDIARY GCE
4766
MATHEMATICS (MEI)
Statistics 1
QUESTION PAPER
Candidates answer on the Printed Answer Book
OCR Supplied Materials:
•
Printed Answer Book 4766
•
MEI Examination Formulae and Tables (MF2)
Monday 19 January 2009
Afternoon
Duration: 1 hour 30 minutes
Other Materials Required:
•
Scientific or graphical calculator
INSTRUCTIONS TO CANDIDATES
These instructions are the same on the Printed Answer Book and the Question Paper.
•
•
•
•
•
•
•
•
•
Write your name clearly in capital letters, your Centre Number and Candidate Number in the spaces provided
on the Printed Answer Book.
The questions are on the inserted Question Paper.
Write your answer to each question in the space provided in the Printed Answer Book. Additional paper
may be used if necessary but you must clearly show your Candidate Number, Centre Number and question
number(s).
Use black ink. Pencil may be used for graphs and diagrams only.
Read each question carefully and make sure that you know what you have to do before starting your answer.
Answer all the questions.
Do not write in the bar codes.
You are permitted to use a graphical calculator in this paper.
Final answers should be given to a degree of accuracy appropriate to the context.
INFORMATION FOR CANDIDATES
This information is the same on the Printed Answer Book and the Question Paper.
•
•
•
•
The number of marks is given in brackets [ ] at the end of each question or part question on the Question
Paper.
You are advised that an answer may receive no marks unless you show sufficient detail of the working to
indicate that a correct method is being used.
The total number of marks for this paper is 72.
The Printed Answer Book consists of 12 pages. The Question Paper consists of 8 pages. Any blank pages
are indicated.
INSTRUCTION TO EXAMS OFFICER / INVIGILATOR
•
Do not send this Question Paper for marking; it should be retained in the centre or destroyed.
© OCR 2009 [H/102/2650]
FP–0C18
OCR is an exempt Charity
Turn over
2
Section A (36 marks)
1
A supermarket chain buys a batch of 10 000 scratchcard draw tickets for sale in its stores. 50 of these
tickets have a £10 prize, 20 of them have a £100 prize, one of them has a £5000 prize and all of the
rest have no prize. This information is summarised in the frequency table below.
Prize money
Frequency
£0
£10
£100
£5000
9929
50
20
1
(i) Find the mean and standard deviation of the prize money per ticket.
[4]
(ii) I buy two of these tickets at random. Find the probability that I win either two £10 prizes or two
£100 prizes.
[3]
2
Thomas has six tiles, each with a different letter of his name on it.
(i) Thomas arranges these letters in a random order. Find the probability that he arranges them in
the correct order to spell his name.
[2]
(ii) On another occasion, Thomas picks three of the six letters at random. Find the probability that
he picks the letters T, O and M (in any order).
[3]
3
A zoologist is studying the feeding behaviour of a group of 4 gorillas. The random variable X
represents the number of gorillas that are feeding at a randomly chosen moment. The probability
distribution of X is shown in the table below.
r
0
1
2
3
4
P(X = r)
p
0.1
0.05
0.05
0.25
(i) Find the value of p.
[1]
(ii) Find the expectation and variance of X .
[5]
(iii) The zoologist observes the gorillas on two further occasions. Find the probability that there are
at least two gorillas feeding on both occasions.
[2]
4
A pottery manufacturer makes teapots in batches of 50. On average 3% of teapots are faulty.
(i) Find the probability that in a batch of 50 there is
(A) exactly one faulty teapot,
[3]
(B) more than one faulty teapot.
[3]
(ii) The manufacturer produces 240 batches of 50 teapots during one month. Find the expected
number of batches which contain exactly one faulty teapot.
[2]
© OCR 2009
4766 Jan09
3
5
Each day Anna drives to work.
• R is the event that it is raining.
• L is the event that Anna arrives at work late.
You are given that P(R) = 0.36, P(L) = 0.25 and P(R ∩ L) = 0.2.
(i) Determine whether the events R and L are independent.
[2]
(ii) Draw a Venn diagram showing the events R and L. Fill in the probability corresponding to each
of the four regions of your diagram.
[3]
(iii) Find P(L | R). State what this probability represents.
[Question 6 is printed overleaf.]
© OCR 2009
4766 Jan09
[3]
4
Section B (36 marks)
6
The temperature of a supermarket fridge is regularly checked to ensure that it is working correctly.
Over a period of three months the temperature (measured in degrees Celsius) is checked 600 times.
These temperatures are displayed in the cumulative frequency diagram below.
600
Cumulative frequency
500
400
300
200
100
0
3.0
3.2
3.4
3.6
3.8
4.0
4.2
4.4
4.6
4.8
5.0
Temperature (degrees Celsius)
(i) Use the diagram to estimate the median and interquartile range of the data.
[3]
(ii) Use your answers to part (i) to show that there are very few, if any, outliers in the sample.
[4]
(iii) Suppose that an outlier is identified in these data. Discuss whether it should be excluded from
any further analysis.
[2]
(iv) Complete the frequency table for these data.
Temperature
(t degrees Celsius)
3.0 ≤ t ≤ 3.4
3.4 < t ≤ 3.8
Frequency
(v) Use your table to calculate an estimate of the mean.
[3]
3.8 < t ≤ 4.2
4.2 < t ≤ 4.6
243
157
4.6 < t ≤ 5.0
[2]
(vi) The standard deviation of the temperatures in degrees Celsius is 0.379. The temperatures are
converted from degrees Celsius into degrees Fahrenheit using the formula F = 1.8C + 32. Hence
estimate the mean and find the standard deviation of the temperatures in degrees Fahrenheit. [3]
© OCR 2009
4766 Jan09
5
7
An online shopping company takes orders through its website. On average 80% of orders from the
website are delivered within 24 hours. The quality controller selects 10 orders at random to check
when they are delivered.
(i) Find the probability that
(A) exactly 8 of these orders are delivered within 24 hours,
[3]
(B) at least 8 of these orders are delivered within 24 hours.
[2]
The company changes its delivery method. The quality controller suspects that the changes will mean
that fewer than 80% of orders will be delivered within 24 hours. A random sample of 18 orders is
checked and it is found that 12 of them arrive within 24 hours.
(ii) Write down suitable hypotheses and carry out a test at the 5% significance level to determine
whether there is any evidence to support the quality controller’s suspicion.
[7]
(iii) A statistician argues that it is possible that the new method could result in either better or worse
delivery times. Therefore it would be better to carry out a 2-tail test at the 5% significance level.
State the alternative hypothesis for this test. Assuming that the sample size is still 18, find the
critical region for this test, showing all of your calculations.
[7]
© OCR 2009
4766 Jan09
6
BLANK PAGE
© OCR 2009
4766 Jan09
7
BLANK PAGE
© OCR 2009
4766 Jan09
8
Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable
effort has been made by the publisher (OCR) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be
pleased to make amends at the earliest possible opportunity.
OCR is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES),
which is itself a department of the University of Cambridge.
© OCR 2009
4766 Jan09
ADVANCED SUBSIDIARY GCE
4766
MATHEMATICS (MEI)
Statistics 1
PRINTED ANSWER BOOK
Candidates answer on this Printed Answer Book
Monday 19 January 2009
Afternoon
OCR Supplied Materials:
• Question Paper 4766 (inserted)
• MEI Examination Formulae and Tables (MF2)
Duration: 1 hour 30 minutes
Other Materials Required:
• Scientific or graphical calculator
*4766*
*
Candidate
Forename
Candidate
Surname
Centre Number
Candidate Number
4
7
6
6
*
INSTRUCTIONS TO CANDIDATES
These instructions are the same on the Printed Answer Book and the Question Paper.
•
•
•
•
•
•
•
•
•
Write your name clearly in capital letters, your Centre Number and Candidate Number in the spaces provided
on the Printed Answer Book.
The questions are on the inserted Question Paper.
Write your answer to each question in the space provided in the Printed Answer Book. Additional paper
may be used if necessary but you must clearly show your Candidate Number, Centre Number and question
number(s).
Use black ink. Pencil may be used for graphs and diagrams only.
Read each question carefully and make sure that you know what you have to do before starting your answer.
Answer all the questions.
Do not write in the bar codes.
You are permitted to use a graphical calculator in this paper.
Final answers should be given to a degree of accuracy appropriate to the context.
INFORMATION FOR CANDIDATES
This information is the same on the Printed Answer Book and the Question Paper.
•
•
•
•
The number of marks is given in brackets [ ] at the end of each question or part question on the Question
Paper.
You are advised that an answer may receive no marks unless you show sufficient detail of the working to
indicate that a correct method is being used.
The total number of marks for this paper is 72.
The Printed Answer Book consists of 12 pages. The Question Paper consists of 8 pages. Any blank pages
are indicated.
© OCR 2009 [H/102/2650]
FP–0C18
OCR is an exempt Charity
Turn over
2
Section A (36 marks)
1 (i)
1 (ii)
© OCR 2009
3
2 (i)
2 (ii)
© OCR 2009
Turn over
4
3 (i)
3 (ii)
3 (iii)
© OCR 2009
5
4 (i) (A)
4 (i) (B)
4 (ii)
© OCR 2009
Turn over
6
5 (i)
5 (ii)
5 (iii)
© OCR 2009
7
Section B (36 marks)
6 (i)
6 (ii)
6 (iii)
© OCR 2009
Turn over
8
6 (iv)
Temperature
(t degrees Celsius)
Frequency
6 (v)
© OCR 2009
3.0 ≤ t ≤ 3.4
3.4 < t ≤ 3.8
3.8 < t ≤ 4.2
4.2 < t ≤ 4.6
243
157
4.6 < t ≤ 5.0
9
6 (vi)
© OCR 2009
Turn over
10
7 (i) (A)
7 (i) (B)
© OCR 2009
11
7 (ii)
© OCR 2009
Turn over
12
7 (iii)
Copyright Information
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whose work is used in this paper. To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced in the OCR Copyright
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OCR is part of the Cambridge Assessment Group; Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a
department of the University of Cambridge.
© OCR 2009